School officials in the nation’s capital failed to collect most of the tuition they were owed from families outside the city whose children attend public schools and allowed those students to remain in the system even when their parents defaulted on payment agreements, according to a D.C. inspector general’s audit.

The audit, released Tuesday by Inspector General Daniel W. Lucas, portrays inadequate record-keeping and lax enforcement of laws against fraudulent enrollment by nonresident families at the Office of the State Superintendent of Education — the oversight agency that monitors both the city’s traditional schools and public charter schools.

In two-thirds of the 67 residency-fraud investigations Lucas examined, the superintendent’s office settled its cases for “much less than the full tuition due” and was unable to provide auditors with records of its investigations. And 51 of 79 nonresident students were allowed to continue attending D.C. schools free because the agency did not alert school administrators that their parents or guardians defaulted on tuition payments.

As a result, the District is owed at least $551,000 in tuition from the families of students who live outside the city, auditors found.

“Maintaining integrity in the admissions process of non-residents into District of Columbia school systems ensures that residents receive priority access to public education in the District of Columbia,” the audit states. “A continued lack of controls over residency verification and payment of non-resident tuition will result in the District continuing to provide tuition-free education to ineligible students.”

Auditors also found the superintendent’s office did not consistently report allegations of residency fraud by government workers — which The Washington Post reported this week occurs routinely and often involves employees of the school system — to the D.C. Board of Ethics and Government Accountability. They also said that the superintendent did not coordinate adequately with the D.C. Office of the Attorney General to decide which cases should be settled and which pursued under the city’s False Claims Act and that it did not effectively track their own cases.

For example, auditors noted that while OSSE used color-coded spreadsheets to track residency-fraud allegations, “there was no guide or legend to identify what a specific color meant, which would help to distinguish the status of the allegations.”

Officials in D.C. Public Schools and the superintendent’s office largely agreed with the auditors’ findings. However, they noted a law they were criticized for not enforcing — the requirement that many nonresident families pay tuition in full before the beginning of the school year — was repealed last year, giving the agency more flexibility to set extended payment plans for parents.

In a written response to the inspector general’s office, State Superintendent of Education Hanseul Kang said her office had begun more in-depth auditing of student residency during the current school year and was in the process of hiring two additional residency-fraud investigators.

And she suggested that improper enrollments are actually a compliment. “It’s a mark of the fast improvement of our schools, the beauty and quality of our school facilities, and the diversity of educational offerings that non-residents are going to such lengths to enroll their children in our schools,” Kang wrote.

Anu Rangappa, a spokeswoman for Mayor Muriel E. Bowser (D), said Kang’s office has created “a more rigorous process to uncover fraud” and noted that the mayor’s budget for the coming fiscal year includes $300,000 in new funding for residency investigations. “Under the superintendent’s leadership, we are making progress, but we have more work to do,” Rangappa said.

D.C. Council member Charles Allen (D-Ward 6) said the audit’s conclusion “just eats away at and undermines parent confidence” in the school system. He questioned whether responsibility for residency-fraud investigations should be moved to the attorney general’s office, which now handles cases only when they have been completed and are ready for settlement or court action.

Council member and education committee chairman David Grosso (I-At Large) praised Kang for acknowledging the need for improvement and said he would bring up residency fraud with the superintendent when she testifies at a budget hearing next week. However, he cautioned against enforcing residency rules in a way that would exclude students who are homeless or live in unstable families.

“While there are certainly cases of those defrauding the system, we must balance the need for rigorous enforcement with the need to provide educational opportunities to our most disadvantaged students,” Grosso said in a written statement.

The findings come as Kang and her staff have come under growing scrutiny. Parents and D.C. Council members have repeatedly questioned the agency’s transparency and the accuracy of its data on school performance in the wake of revelations that a third of last year’s high school graduates should not have received diplomas because of chronic truancy and other problems.

In February, The Post reported an attorney in the superintendent’s office told those handling a previously undisclosed investigation into potentially widespread residency fraud at the renowned Duke Ellington School of the Arts to “take your time” because of the risk of negative publicity during a mayoral election year.

Kang, whom Bowser appointed in 2015, said at the time that any such comment by a member of her staff was “absolutely unacceptable” and that the matter would be investigated.

This week, The Post reported the school system has a single investigator for its 92,000 students and Kang and her staff were unable to provide basic details about their efforts to stop residency fraud, such as how much money they have collected from nonresidents or which staffers are responsible for ensuring parents pay tuition.

Kang said much of that disorganization predated her tenure and the office was now updating and strengthening its approach to residency fraud.

“This is an area that we’ve known is an area we need to improve on, and we’ve been working on putting these systems in place,” she said.